In golf betting, +1000 odds means a $100 bet would pay out $1,100 in profit ($1,000 plus the $100 bet). This is most common when betting on a player to win outright. For instance, Rory McIlroy might have +1000 odds to win the Masters in 2024. A player could also have +1000 odds to win the tournament in live betting.

So when you see a book offer a Risk-Free Bet Up to $1,000  it simply means that if you lose you'll get the amount of your initial wager back in something other than cash, and if you win, the book has decided that you don't really deserve anything extra.